Tikhonov regularization in Hilbert scales under conditional stability assumptions

被引：23

作者：

Egger, H. ^{[1
]}

Hofmann, B. ^{[2
]}

机构：

[1] Tech Univ Darmstadt, Dept Math, Dolivostr 15, D-64293 Darmstadt, Germany

[2] TU Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

INVERSE PROBLEMS | 2018年 / 34卷 / 11期

关键词：

nonlinear inverse problems; conditional stability; Tikhonov regularization; discrepancy principle; convergence rates; Hilbert scales; ILL-POSED PROBLEMS;

D O I：

10.1088/1361-6420/aadef4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Conditional stability estimates allow us to characterize the degree of illposedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here consider the stable solution of nonlinear inverse problems satisfying a conditional stability estimate by Tikhonov regularization in Hilbert scales. Order optimal convergence rates are established for a priori and a posteriori parameter choice strategies. The role of a hidden source condition is investigated and the relation to previous results for regularization in Hilbert scales is elaborated. The applicability of the results is discussed for some model problems, and the theoretical results are illustrated by numerical tests.

引用

页数：17

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